For a 4x game, should the map be somewhat symmetrical or irregular. By irregular I mean the stars are organized in random, like the map is in no way symmetrical. By symmetrical I mean that both sides of the map are basically copies of one another.

Symmetrical: Attempts to provide some sort of 'balance' between people if they start in opposite areas. This can be good if it's a competitive (Meaning against other players) since it allows for less issues dealing with 'starting balance'. You both have the opportunity to get the same stuff, so if you don't, it's an issue of playing badly, etc.

Irregular: Allows for more fun/interesting layouts, especially if there's a resource system within the game. If you start out with a lot, you're lucky, but you're also more of a target, etc. However, it can lead to the difference between a steam-roll game and one that takes forever to get through. Think Civilization: If you start out near early age resources, you can advance quicker and steam-roll through. If you don't, you can still win, but it's a long, hard slog.

For a 4x game, should the map be somewhat symmetrical or irregular. By irregular I mean the stars are organized in random, like the map is in no way symmetrical. By symmetrical I mean that both sides of the map are basically copies of one another.

I'm not sure what kind of space strategy game you are making, but I think you may need a different kind of "symmetry" instead of a symmetric layout of stars. One thing that is often bugging me in space 4X games is that you may have basically lost at the beginning of the game since there's no inhabitable/rich/good planets nearby. Maybe an option is to guarantee somehow that each player has a number of suitable planets nearby? (as in: create some) But then again, some people like that kind of randomness. Maybe you can let the players choose?

I'd also think about symmetry in more levels than just the position of starts/planets. You could, for example, have a symmetrically balanced star map where the parts with lesser star density have better planets or resources, while dense star clusters are composed of small resources in greater number.

Visually, the map will look asymmetrical and interesting, even though internally it is symmetrical.

It helps to assign everything in your game a certain numerical value, and add it all up to see if it is balanced. Kind of like placing objects of different sizes and densities on an scale.

Why not divide the map in 2/3/4/n players, throw a random "stars" number per player, randomize the positions of those in each sector of the map, so every player gets the same amount of stars in his sector and none of them are equally to another (at least not by locations of stars). You do understand what I mean?

So I guess the map's attributes should be player's choice in 4x games.

Only for "custom map". Don't make the player customize attributes out of the box, just aim for some sensible distribution like some of the suggestions above. Also consider that you can scan for good player starting positions too, so it doesn't have to be done 100% at map generation time.

So I guess the map's attributes should be player's choice in 4x games.

Not necessarily, but it is often good to have some choice. However, I must say that sometimes I find that too many settings takes me out of the immersion of a 4X space strategy game. Especially when I have to choose my opponents (and their AI settings), that takes away much of the fun of discovery.

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